A Review of Mathematical Models for Tumor Dynamics and Treatment Resistance Evolution of Solid Tumors

Agent-based modeling in cancer biomedicine: applications and tools for calibration and validation

Computational models are not just appealing because they can simulate and predict the development of biological phenomena across multiple spatial and temporal scales, but also because they can integrate information from well-established in vitro and in vivo models and test new hypotheses in cancer biomedicine. Agent-based models and simulations are especially interesting candidates among computational modeling procedures in cancer research due to the capability to, for instance, recapitulate the dynamics of neoplasia and tumor - host interactions. Yet, the absence of methods to validate the consistency of the results across scales can hinder adoption by turning fine-tuned models into black boxes. This review compiles relevant literature that explores strategies to leverage high-fidelity simulations of multi-scale, or multi-level, cancer models with a focus on verification approached as simulation calibration. We consolidate our review with an outline of modern approaches for agent-based models' validation and provide an ambitious outlook toward rigorous and reliable calibration.

Assessing tumor volumetric reduction with consideration for setup errors based on mathematical tumor model and microdosimetric kinetic model in single-isocenter VMAT for brain metastases

The volumetric reduction rate (VRR) was evaluated with consideration for six degrees-of-freedom (6DoF) patient setup errors based on a mathematical tumor model in single-isocenter volumetric modulated arc therapy (SI-VMAT) for brain metastases. Simulated gross tumor volumes (GTV) of 1.0 cm and dose distribution were created (27 Gy/3 fractions). The distance between the GTV center and isocenter (d) was set at 0-10 cm. The GTV was translated within 0-1.0 mm (Trans) and rotated within 0-1.0° (Rot) in the three axis directions using affine transformation. The tumor growth volume was calculated using a multicomponent mathematical model (MCTM), and lethal effects of irradiation and repair from damage during irradiation were calculated by a microdosimetric kinetic model (MKM) for non-small cell lung cancer (NSCLC) A549 and NCI-H460 (H460) cells. The VRRs were calculated 5 days after the end of irradiation using the physical dose to the GTV for varying d and 6DoF setup errors. The tolerance value of VRR, the GTV volume reduction rate, was set at 5%, based on the pre-irradiation GTV volume. With the exception of the only one A549 condition where (Trans, Rot) = (1.0 mm, 1.0°) was repeated for 3 fractions, all conditions met all the tolerance VRR values for A549 and H460 cells with varying d from 0 to 10 cm. Evaluation based on the mathematical tumor model suggested that if the 6DoF setup errors at each irradiation could be kept within 1.0 mm and 1.0°, there would be little effect on tumor volume regardless of the distance from the isocenter in SI-VMAT.

Joint modeling of tumor dynamics and progression-free survival in advanced breast cancer: Leveraging data from amcenestrant early phase I-II trials

A joint modeling framework was developed using data from 75 patients of early amcenestrant phase I-II AMEERA-1-2 dose escalation and expansion cohorts. A semi-mechanistic tumor growth inhibition (TGI) model was developed. It accounts for the dynamics of sensitive and resistant tumor cells, an exposure-driven effect on tumor proliferation of sensitive cells, and a delay in the initiation of treatment effect to describe the time course of target lesion tumor size (TS) data. Individual treatment exposure overtime was introduced in the model using concentrations predicted by a population pharmacokinetic model of amcenestrant. This joint modeling framework integrated complex RECISTv1.1 criteria information, linked TS metrics to progression-free survival (PFS), and was externally evaluated using the randomized phase II trial AMEERA-3. We demonstrated that the instantaneous rate of change in TS (TS slope) was an important predictor of PFS and the developed joint model was able to predict well the PFS of amcenestrant phase II monotherapy trial using only early phase I-II data. This provides a good modeling and simulation tool to inform early development decisions.

Morphological Stability for in silico Models of Avascular Tumors

The landscape of computational modeling in cancer systems biology is diverse, offering a spectrum of models and frameworks, each with its own trade-offs and advantages. Ideally, models are meant to be useful in refining hypotheses, to sharpen experimental procedures and, in the longer run, even for applications in personalized medicine. One of the greatest challenges is to balance model realism and detail with experimental data to eventually produce useful data-driven models. We contribute to this quest by developing a transparent, highly parsimonious, first principle in silico model of a growing avascular tumor. We initially formulate the physiological considerations and the specific model within a stochastic cell-based framework. We next formulate a corresponding mean-field model using partial differential equations which is amenable to mathematical analysis. Despite a few notable differences between the two models, we are in this way able to successfully detail the impact of all parameters in the stability of the growth process and on the eventual tumor fate of the stochastic model. This facilitates the deduction of Bayesian priors for a given situation, but also provides important insights into the underlying mechanism of tumor growth and progression. Although the resulting model framework is relatively simple and transparent, it can still reproduce the full range of known emergent behavior. We identify a novel model instability arising from nutrient starvation and we also discuss additional insight concerning possible model additions and the effects of those. Thanks to the framework's flexibility, such additions can be readily included whenever the relevant data become available.

From immune equilibrium to tumor ecodynamics

Objectives

There is no theory to quantitatively describe the complex tumor ecosystem. At the same time, cancer immunotherapy is considered a revolution in oncology, but the methods used to describe tumors and the criteria used to evaluate efficacy are not keeping pace. The purpose of this study is to establish a new theory for quantitatively describing the tumor ecosystem, innovating the methods of tumor characterization, and establishing new efficacy evaluation criteria for cancer immunotherapy.

Methods

Based on the mathematization of immune equilibrium theory and the establishment of immunodynamics in a previous study, the method of reverse immunodynamics was used, namely, the immune braking force was regarded as the tumor ecological force and the immune force was regarded as the tumor ecological braking force, and the concept of momentum in physics was applied to the tumor ecosystem to establish a series of tumor ecodynamic equations. These equations were used to solve the fundamental and applied problems of the complex tumor ecosystem.

Results

A series of tumor ecodynamic equations were established. The tumor ecological momentum equations and their component factors could be used to distinguish disease progression, pseudoprogression, and hyperprogression in cancer immunotherapy. On this basis, the adjusted tumor momentum equations were established to achieve the equivalence of tumor activity (including immunosuppressive activity and metabolic activity) and tumor volume, which could be used to calculate individual disease remission rate and establish new efficacy evaluation criteria (ieRECIST) for immunotherapy of solid tumor based on tumor ecodynamics. At the same time, the concept of moving cube-to-force square ratio and its expression were proposed to calculate the area under the curve of tumor ecological braking force of blood required to achieve an individual disease remission rate when the adjusted tumor ecological momentum was known.

Conclusions

A new theory termed tumor ecodynamics emphasizing both tumor activity and tumor volume is established to solve a series of basic and applied problems in the complex tumor ecosystem. It can be predicted that the future will be the era of cancer immune ecotherapy that targets the entire tumor ecosystem.

Medical Relevance, State-of-the-Art and Perspectives of "Sweet Metacode" in Liquid Biopsy Approaches

This review briefly introduces readers to an area where glycomics meets modern oncodiagnostics with a focus on the analysis of sialic acid (Neu5Ac)-terminated structures. We present the biochemical perspective of aberrant sialylation during tumourigenesis and its significance, as well as an analytical perspective on the detection of these structures using different approaches for diagnostic and therapeutic purposes. We also provide a comparison to other established liquid biopsy approaches, and we mathematically define an early-stage cancer based on the overall prognosis and effect of these approaches on the patient's quality of life. Finally, some barriers including regulations and quality of clinical validations data are discussed, and a perspective and major challenges in this area are summarised.

Impact of Resistance on Therapeutic Design: A Moran Model of Cancer Growth

Resistance of cancers to treatments, such as chemotherapy, largely arise due to cell mutations. These mutations allow cells to resist apoptosis and inevitably lead to recurrence and often progression to more aggressive cancer forms. Sustained-low dose therapies are being considered as an alternative over maximum tolerated dose treatments, whereby a smaller drug dosage is given over a longer period of time. However, understanding the impact that the presence of treatment-resistant clones may have on these new treatment modalities is crucial to validating them as a therapeutic avenue. In this study, a Moran process is used to capture stochastic mutations arising in cancer cells, inferring treatment resistance. The model is used to predict the probability of cancer recurrence given varying treatment modalities. The simulations predict that sustained-low dose therapies would be virtually ineffective for a cancer with a non-negligible probability of developing a sub-clone with resistance tendencies. Furthermore, calibrating the model to in vivo measurements for breast cancer treatment with Herceptin, the model suggests that standard treatment regimens are ineffective in this mouse model. Using a simple Moran model, it is possible to explore the likelihood of treatment success given a non-negligible probability of treatment resistant mutations and suggest more robust therapeutic schedules.

A review of mechanistic learning in mathematical oncology

Mechanistic learning refers to the synergistic combination of mechanistic mathematical modeling and data-driven machine or deep learning. This emerging field finds increasing applications in (mathematical) oncology. This review aims to capture the current state of the field and provides a perspective on how mechanistic learning may progress in the oncology domain. We highlight the synergistic potential of mechanistic learning and point out similarities and differences between purely data-driven and mechanistic approaches concerning model complexity, data requirements, outputs generated, and interpretability of the algorithms and their results. Four categories of mechanistic learning (sequential, parallel, extrinsic, intrinsic) of mechanistic learning are presented with specific examples. We discuss a range of techniques including physics-informed neural networks, surrogate model learning, and digital twins. Example applications address complex problems predominantly from the domain of oncology research such as longitudinal tumor response predictions or time-to-event modeling. As the field of mechanistic learning advances, we aim for this review and proposed categorization framework to foster additional collaboration between the data- and knowledge-driven modeling fields. Further collaboration will help address difficult issues in oncology such as limited data availability, requirements of model transparency, and complex input data which are embraced in a mechanistic learning framework.

A Mathematical Model of Stroma-Supported Allometric Tumor Growth

Mounting empirical research suggests that the stroma, or interface between healthy and cancerous tissue, is a critical determinate of cancer invasion. At the same time, a cancer cell's location and potential to proliferate can influence its sensitivity to cancer treatments. In this paper, we use ordinary differential equations to develop spatially structured models for solid tumors wherein the growth of tumor components is coordinated. The model tumors feature two components, a proliferating peripheral growth region, which potentially includes a mix of cancerous and noncancerous stroma cells, and a solid tumor core. Mathematical and numerical analysis are used to investigate how coordinated expansion of the tumor growth region and core can influence overall growth dynamics in a variety of tumor types. Model assumptions, which are motivated by empirical and in silico solid tumor research, are evaluated through comparison to tumor volume data and existing models of tumor growth.

Focused ultrasound ablation of melanoma with boiling histotripsy yields abscopal tumor control and antigen-dependent dendritic cell activation

Background: Boiling histotripsy (BH), a mechanical focused ultrasound ablation strategy, can elicit intriguing signatures of anti-tumor immunity. However, the influence of BH on dendritic cell function is unknown, compromising our ability to optimally combine BH with immunotherapies to control metastatic disease. Methods: BH was applied using a sparse scan (1 mm spacing between sonications) protocol to B16F10-ZsGreen melanoma in bilateral and unilateral settings. Ipsilateral and contralateral tumor growth was measured. Flow cytometry was used to track ZsGreen antigen and assess how BH drives dendritic cell behavior. Results: BH monotherapy elicited ipsilateral and abscopal tumor control in this highly aggressive model. Tumor antigen presence in immune cells in the tumor-draining lymph nodes (TDLNs) was ~3-fold greater at 24h after BH, but this abated by 96h. B cells, macrophages, monocytes, granulocytes, and both conventional dendritic cell subsets (i.e. cDC1s and cDC2s) acquired markedly more antigen with BH. BH drove activation of both cDC subsets, with activation being dependent upon tumor antigen acquisition. Our data also suggest that BH-liberated tumor antigen is complexed with damage-associated molecular patterns (DAMPs) and that cDCs do not traffic to the TDLN with antigen. Rather, they acquire antigen as it flows through afferent lymph vessels into the TDLN. Conclusion: When applied with a sparse scan protocol, BH monotherapy elicits abscopal melanoma control and shapes dendritic cell function through several previously unappreciated mechanisms. These results offer new insight into how to best combine BH with immunotherapies for the treatment of metastatic melanoma.

Focused ultrasound ablation of melanoma with boiling histotripsy yields abscopal tumor control and antigen-dependent dendritic cell activation

Background

Boiling histotripsy (BH), a mechanical focused ultrasound ablation strategy, can elicit intriguing signatures of anti-tumor immunity. However, the influence of BH on dendritic cell function is unknown, compromising our ability to optimally combine BH with immunotherapies to control metastatic disease.

Methods

BH was applied using a sparse scan (1 mm spacing between sonications) protocol to B16F10-ZsGreen melanoma in bilateral and unilateral settings. Ipsilateral and contralateral tumor growth was measured. Flow cytometry was used to track ZsGreen antigen and assess how BH drives dendritic cell behavior.

Results

BH monotherapy elicited ipsilateral and abscopal tumor control in this highly aggressive model. Tumor antigen presence in immune cells in the tumor-draining lymph nodes (TDLNs) was ~3-fold greater at 24h after BH, but this abated by 96h. B cells, macrophages, monocytes, granulocytes, and both conventional dendritic cell subsets (i.e. cDC1s and cDC2s) acquired markedly more antigen with BH. BH drove activation of both cDC subsets, with activation being dependent upon tumor antigen acquisition. Our data also suggest that BH-liberated tumor antigen is complexed with damage-associated molecular patterns (DAMPs) and that cDCs do not traffic to the TDLN with antigen. Rather, they acquire antigen as it flows through afferent lymph vessels into the TDLN.

Conclusion

When applied with a sparse scan protocol, BH monotherapy elicits abscopal melanoma control and shapes dendritic cell function through several previously unappreciated mechanisms. These results offer new insight into how to best combine BH with immunotherapies for the treatment of metastatic melanoma.

Nonlinear multilevel joint model for individual lesion kinetics and survival to characterize intra-individual heterogeneity in patients with advanced cancer

In advanced cancer patients, tumor burden is calculated using the sum of the longest diameters (SLD) of the target lesions, a measure that lumps all lesions together and ignores intra-patient heterogeneity. Here, we used a rich dataset of 342 metastatic bladder cancer patients treated with a novel immunotherapy agent to develop a Bayesian multilevel joint model that can quantify heterogeneity in lesion dynamics and measure their impact on survival. Using a nonlinear model of tumor growth inhibition, we estimated that dynamics differed greatly among lesions, and inter-lesion variability accounted for 21% and 28% of the total variance in tumor shrinkage and treatment effect duration, respectively. Next, we investigated the impact of individual lesion dynamics on survival. Lesions located in the liver and in the bladder had twice as much impact on the instantaneous risk of death compared to those located in the lung or the lymph nodes. Finally, we evaluated the utility of individual lesion follow-up for dynamic predictions. Consistent with results at the population level, the individual lesion model outperformed a model relying only on SLD, especially at early landmark times and in patients with liver or bladder target lesions. Our results show that an individual lesion model can characterize the heterogeneity in tumor dynamics and its impact on survival in advanced cancer patients.

Explainable deep learning for tumor dynamic modeling and overall survival prediction using Neural-ODE

While tumor dynamic modeling has been widely applied to support the development of oncology drugs, there remains a need to increase predictivity, enable personalized therapy, and improve decision-making. We propose the use of Tumor Dynamic Neural-ODE (TDNODE) as a pharmacology-informed neural network to enable model discovery from longitudinal tumor size data. We show that TDNODE overcomes a key limitation of existing models in its ability to make unbiased predictions from truncated data. The encoder-decoder architecture is designed to express an underlying dynamical law that possesses the fundamental property of generalized homogeneity with respect to time. Thus, the modeling formalism enables the encoder output to be interpreted as kinetic rate metrics, with inverse time as the physical unit. We show that the generated metrics can be used to predict patients' overall survival (OS) with high accuracy. The proposed modeling formalism provides a principled way to integrate multimodal dynamical datasets in oncology disease modeling.

Quantifying the potential benefits of early detection for pancreatic cancer through a counterfactual simulation modeling analysis

The benefits of cancer early detection depend on various factors, including cancer type, screening method performance, stage at diagnosis, and subsequent treatment. Although numerous studies have evaluated the effectiveness of screening interventions for identifying cancer at earlier stages, there is no quantitative analysis that studies the optimal early detection time interval that results in the greatest mortality benefit; such data could serve as a target and benchmark for cancer early detection strategies. In this study, we focus on pancreatic ductal adenocarcinoma (PDAC), a cancer known for its lack of early symptoms. Consequently, it is most often detected at late stages when the 5-year survival rate is only 3%. We developed a PDAC population model that simulates an individual patient's age and stage at diagnosis, while replicating overall US cancer incidence and mortality rates. The model includes "cancer sojourn time," serving as a proxy for the speed of cancer progression, with shorter times indicating rapid progression and longer times indicating slower progression. In our PDAC model, our hypothesis was that earlier cancer detection, potentially through a hypothetical screening intervention in the counterfactual analysis, would yield reduced mortality as compared to a no-screening group. We found that the benefits of early detection, such as increased life-years gained, are greater when the sojourn time is shorter, reaching their maximum when identification is made 4-6 years prior to clinical diagnosis (e.g., when a symptomatic diagnosis is made). However, when early detection occurs even earlier, for example 6-10 years prior to clinical diagnosis, the benefits significantly diminish for shorter sojourn time cancers, and level off for longer sojourn time cancers. Our study clarifies the potential benefits of PDAC early detection that explicitly incorporates individual patient heterogeneity in cancer progression and identifies quantitative benchmarks for future interventions.

Modelling Keloids Dynamics: A Brief Review and New Mathematical Perspectives

Keloids are fibroproliferative disorders described by excessive growth of fibrotic tissue, which also invades adjacent areas (beyond the original wound borders). Since these disorders are specific to humans (no other animal species naturally develop keloid-like tissue), experimental in vivo/in vitro research has not led to significant advances in this field. One possible approach could be to combine in vitro human models with calibrated in silico mathematical approaches (i.e., models and simulations) to generate new testable biological hypotheses related to biological mechanisms and improved treatments. Because these combined approaches do not really exist for keloid disorders, in this brief review we start by summarising the biology of these disorders, then present various types of mathematical and computational approaches used for related disorders (i.e., wound healing and solid tumours), followed by a discussion of the very few mathematical and computational models published so far to study various inflammatory and mechanical aspects of keloids. We conclude this review by discussing some open problems and mathematical opportunities offered in the context of keloid disorders by such combined in vitro/in silico approaches, and the need for multi-disciplinary research to enable clinical progress.

Mathematical model combined with microdosimetric kinetic model for tumor volume calculation in stereotactic body radiation therapy

We proposed a new mathematical model that combines an ordinary differential equation (ODE) and microdosimetric kinetic model (MKM) to predict the tumor-cell lethal effect of Stereotactic body radiation therapy (SBRT) applied to non-small cell lung cancer (NSCLC). The tumor growth volume was calculated by the ODE in the multi-component mathematical model (MCM) for the cell lines NSCLC A549 and NCI-H460 (H460). The prescription doses 48 Gy/4 fr and 54 Gy/3 fr were used in the SBRT, and the effect of the SBRT on tumor cells was evaluated by the MKM. We also evaluated the effects of (1) linear quadratic model (LQM) and the MKM, (2) varying the ratio of active and quiescent tumors for the total tumor volume, and (3) the length of the dose-delivery time per fractionated dose (tinter) on the initial tumor volume. We used the ratio of the tumor volume at 1 day after the end of irradiation to the tumor volume before irradiation to define the radiation effectiveness value (REV). The combination of MKM and MCM significantly reduced REV at 48 Gy/4 fr compared to the combination of LQM and MCM. The ratio of active tumors and the prolonging of tinter affected the decrease in the REV for A549 and H460 cells. We evaluated the tumor volume considering a large fractionated dose and the dose-delivery time by combining the MKM with a mathematical model of tumor growth using an ODE in lung SBRT for NSCLC A549 and H460 cells.

Clinical trial designs for evaluating and exploiting cancer evolution

The evolution of drug-resistant cell subpopulations causes cancer treatment failure. Current preclinical evidence shows that it is possible to model herding of clonal evolution and collateral sensitivity where an initial treatment could favourably influence the response to a subsequent one. Novel therapy strategies exploiting this understanding are being considered, and clinical trial designs for steering cancer evolution are needed. Furthermore, preclinical evidence suggests that different subsets of drug-sensitive and resistant clones could compete between themselves for nutrients/blood supply, and clones that populate a tumour do so at the expense of other clones. Treatment paradigms based on this clinical application of exploiting cell-cell competition include intermittent dosing regimens or cycling different treatments before progression. This will require clinical trial designs different from the conventional practice of evaluating responses to individual therapy regimens. Next-generation sequencing to assess clonal dynamics longitudinally will improve current radiological assessment of clinical response/resistance and be incorporated into trials exploiting evolution. Furthermore, if understood, clonal evolution can be used to therapeutic advantage, improving patient outcomes based on a new generation of clinical trials.

Multicomponent mathematical model for tumor volume calculation with setup error using single-isocenter stereotactic radiotherapy for multiple brain metastases

We evaluated the tumor residual volumes considering six degrees-of-freedom (6DoF) patient setup errors in stereotactic radiotherapy (SRT) with multicomponent mathematical model using single-isocenter irradiation for brain metastases. Simulated spherical gross tumor volumes (GTVs) with 1.0 (GTV 1), 2.0 (GTV 2), and 3.0 (GTV 3)-cm diameters were used. The distance between the GTV center and isocenter (d) was set at 0-10 cm. The GTV was simultaneously translated within 0-1.0 mm (T) and rotated within 0°-1.0° (R) in the three axis directions using affine transformation. We optimized the tumor growth model parameters using measurements of non-small cell lung cancer cell lines' (A549 and NCI-H460) growth. We calculated the GTV residual volume at the irradiation's end using the physical dose to the GTV when the GTV size, d, and 6DoF setup error varied. The d-values that satisfy tolerance values (10%, 35%, and 50%) of the GTV residual volume rate based on the pre-irradiation GTV volume were determined. The larger the tolerance value set for both cell lines, the longer the distance to satisfy the tolerance value. In GTV residual volume evaluations based on the multicomponent mathematical model on SRT with single-isocenter irradiation, the smaller the GTV size and the larger the distance and 6DoF setup error, the shorter the distance that satisfies the tolerance value might need to be.

Do We Preserve Tumor Control Probability (TCP) in FLASH Radiotherapy? A Model-Based Analysis

Reports of concurrent sparing of normal tissue and iso-effective treatment of tumors at ultra-high dose-rates (uHDR) have fueled the growing field of FLASH radiotherapy. However, iso-effectiveness in tumors is often deduced from the absence of a significant difference in their growth kinetics. In a model-based analysis, we investigate the meaningfulness of these indications for the clinical treatment outcome. The predictions of a previously benchmarked model of uHDR sparing in the "UNIfied and VERSatile bio response Engine" (UNIVERSE) are combined with existing models of tumor volume kinetics as well as tumor control probability (TCP) and compared to experimental data. The potential TCP of FLASH radiotherapy is investigated by varying the assumed dose-rate, fractionation schemes and oxygen concentration in the target. The developed framework describes the reported tumor growth kinetics appropriately, indicating that sparing effects could be present in the tumor but might be too small to be detected with the number of animals used. The TCP predictions show the possibility of substantial loss of treatment efficacy for FLASH radiotherapy depending on several variables, including the fractionation scheme, oxygen level, and DNA repair kinetics. The possible loss of TCP should be seriously considered when assessing the clinical viability of FLASH treatments.

Assessing the Increased Variability in Individual Lesion Kinetics During Immunotherapy: Does It Exist, and Does It Matter?

PURPOSE

Several studies have raised the hypothesis that immunotherapy may exacerbate the variability in individual lesions, increasing the risk of observing divergent kinetic profiles within the same patient. This questions the use of the sum of the longest diameter to follow the response to immunotherapy. Here, we aimed to study this hypothesis by developing a model that estimates the different sources of variability in lesion kinetics, and we used this model to evaluate the impact of this variability on survival.

METHODS

We relied on a semimechanistic model to follow the nonlinear kinetics of lesions and their impact on the risk of death, adjusted on organ location. The model incorporated two levels of random effects to characterize both between- and within-patient variability in response to treatment. The model was estimated on 900 patients from a phase III randomized trial evaluating programmed death-ligand 1 checkpoint inhibitor atezolizumab versus chemotherapy in patients with second-line metastatic urothelial carcinoma (IMvigor211).

RESULTS

The within-patient variability in the four parameters that characterize individual lesion kinetics represented between 12% and 78% of the total variability during chemotherapy. Similar results were obtained during atezolizumab, except for the durability of the treatment effects, for which the within-patient variability was markedly larger than during chemotherapy (40% v 12%, respectively). Accordingly, the occurrence of divergent profile consistently increased over time in patients treated with atezolizumab and was equal to about 20% after 1 year of treatment. Finally, we show that accounting for the within-patient variability provided a better prediction of most at-risk patients than a model relying solely on the sum of the longest diameter.

CONCLUSION

Within-patient variability provides valuable information for the assessment of treatment efficacy and the detection of at-risk patients.

Practical Understanding of Cancer Model Identifiability in Clinical Applications

Mathematical models are a core component in the foundation of cancer theory and have been developed as clinical tools in precision medicine. Modeling studies for clinical applications often assume an individual's characteristics can be represented as parameters in a model and are used to explain, predict, and optimize treatment outcomes. However, this approach relies on the identifiability of the underlying mathematical models. In this study, we build on the framework of an observing-system simulation experiment to study the identifiability of several models of cancer growth, focusing on the prognostic parameters of each model. Our results demonstrate that the frequency of data collection, the types of data, such as cancer proxy, and the accuracy of measurements all play crucial roles in determining the identifiability of the model. We also found that highly accurate data can allow for reasonably accurate estimates of some parameters, which may be the key to achieving model identifiability in practice. As more complex models required more data for identification, our results support the idea of using models with a clear mechanism that tracks disease progression in clinical settings. For such a model, the subset of model parameters associated with disease progression naturally minimizes the required data for model identifiability.

Mapping lesion-specific response and progression dynamics and inter-organ variability in metastatic colorectal cancer

Achieving systemic tumor control across metastases is vital for long-term patient survival but remains intractable in many patients. High lesion-level response heterogeneity persists, conferring many dissociated responses across metastatic lesions. Most studies of metastatic disease focus on tumor molecular and cellular features, which are crucial to elucidating the mechanisms underlying lesion-level variability. However, our understanding of lesion-specific heterogeneity on the macroscopic level, such as lesion dynamics in growth, response, and progression during treatment, remains rudimentary. This study investigates lesion-specific response heterogeneity through analyzing 116,542 observations of 40,612 lesions in 4,308 metastatic colorectal cancer (mCRC) patients. Despite significant differences in their response and progression dynamics, metastatic lesions converge on four phenotypes that vary with anatomical site. Importantly, we find that organ-level progression sequence is closely associated with patient long-term survival, and that patients with the first lesion progression in the liver often have worse survival. In conclusion, our study provides insights into lesion-specific response and progression heterogeneity in mCRC and creates impetus for metastasis-specific therapeutics.

On tumoural growth and treatment under cellular dedifferentiation

Differentiated cancer cells may regain stem cell characteristics; however, the effects of such a cellular dedifferentiation on tumoural growth and treatment are currently understudied. Thus, we here extend a mathematical model of cancer stem cell (CSC) driven tumour growth to also include dedifferentiation. We show that dedifferentiation increases the likelihood of tumorigenesis and the speed of tumoural growth, both modulated by the proliferative potential of the non-stem cancer cells (NSCCs). We demonstrate that dedifferentiation also may lead to treatment evasion, especially when a treatment solely targets CSCs. Conversely, targeting both CSCs and NSCCs in parallel is shown to be more robust to dedifferentiation. Despite dedifferentiation, perturbing CSC-related parameters continues to exert the largest relative effect on tumoural growth; however, we show the existence of synergies between specific CSC- and NSCC-directed treatments which cause superadditive reductions of tumoural growth. Overall, our study demonstrates various effects of dedifferentiation on growth and treatment of tumoural lesions, and we anticipate our results to be helpful in guiding future molecular and clinical research on limiting tumoural growth in vivo.

Mathematical modeling of cancer immunotherapy for personalized clinical translation

Encouraging advances are being made in cancer immunotherapy modeling, especially in the key areas of developing personalized treatment strategies based on individual patient parameters, predicting treatment outcomes and optimizing immunotherapy synergy when used in combination with other treatment approaches. Here we present a focused review of the most recent mathematical modeling work on cancer immunotherapy with a focus on clinical translatability. It can be seen that this field is transitioning from pure basic science to applications that can make impactful differences in patients' lives. We discuss how researchers are integrating experimental and clinical data to fully inform models so that they can be applied for clinical predictions, and present the challenges that remain to be overcome if widespread clinical adaptation is to be realized. Lastly, we discuss the most promising future applications and areas that are expected to be the focus of extensive upcoming modeling studies.

Optimizing combination therapy in a murine model of HER2+ breast cancer

Human epidermal growth factor receptor 2 positive (HER2+) breast cancer is frequently treated with drugs that target the HER2 receptor, such as trastuzumab, in combination with chemotherapy, such as doxorubicin. However, an open problem in treatment design is to determine the therapeutic regimen that optimally combines these two treatments to yield optimal tumor control. Working with data quantifying temporal changes in tumor volume due to different trastuzumab and doxorubicin treatment protocols in a murine model of human HER2+ breast cancer, we propose a complete framework for model development, calibration, selection, and treatment optimization to find the optimal treatment protocol. Through different assumptions for the drug-tumor interactions, we propose ten different models to characterize the dynamic relationship between tumor volume and drug availability, as well as the drug-drug interaction. Using a Bayesian framework, each of these models are calibrated to the dataset and the model with the highest Bayesian information criterion weight is selected to represent the biological system. The selected model captures the inhibition of trastuzumab due to pre-treatment with doxorubicin, as well as the increase in doxorubicin efficacy due to pre-treatment with trastuzumab. We then apply optimal control theory (OCT) to this model to identify two optimal treatment protocols. In the first optimized protocol, we fix the maximum dosage for doxorubicin and trastuzumab to be the same as the maximum dose delivered experimentally, while trying to minimize tumor burden. Within this constraint, optimal control theory indicates the optimal regimen is to first deliver two doses of trastuzumab on days 35 and 36, followed by two doses of doxorubicin on days 37 and 38. This protocol predicts an additional 45% reduction in tumor burden compared to that achieved with the experimentally delivered regimen. In the second optimized protocol we fix the tumor control to be the same as that obtained experimentally, and attempt to reduce the doxorubicin dose. Within this constraint, the optimal regimen is the same as the first optimized protocol but uses only 43% of the doxorubicin dose used experimentally. This protocol predicts tumor control equivalent to that achieved experimentally. These results strongly suggest the utility of mathematical modeling and optimal control theory for identifying therapeutic regimens maximizing efficacy and minimizing toxicity.

Model-informed experimental design recommendations for distinguishing intrinsic and acquired targeted therapeutic resistance in head and neck cancer

The promise of precision medicine has been limited by the pervasive resistance to many targeted therapies for cancer. Inferring the timing (i.e., pre-existing or acquired) and mechanism (i.e., drug-induced) of such resistance is crucial for designing effective new therapeutics. This paper studies cetuximab resistance in head and neck squamous cell carcinoma (HNSCC) using tumor volume data obtained from patient-derived tumor xenografts. We ask if resistance mechanisms can be determined from this data alone, and if not, what data would be needed to deduce the underlying mode(s) of resistance. To answer these questions, we propose a family of mathematical models, with each member of the family assuming a different timing and mechanism of resistance. We present a method for fitting these models to individual volumetric data, and utilize model selection and parameter sensitivity analyses to ask: which member(s) of the family of models best describes HNSCC response to cetuximab, and what does that tell us about the timing and mechanisms driving resistance? We find that along with time-course volumetric data to a single dose of cetuximab, the initial resistance fraction and, in some instances, dose escalation volumetric data are required to distinguish among the family of models and thereby infer the mechanisms of resistance. These findings can inform future experimental design so that we can best leverage the synergy of wet laboratory experimentation and mathematical modeling in the study of novel targeted cancer therapeutics.

Growth‐rate model predicts in vivo tumor response from in vitro data

A major challenge in oncology drug development is to elucidate why drugs that show promising results in cancer cell lines in vitro fail in mouse studies or human trials. One of the fundamental steps toward solving this problem is to better predict how in vitro potency translates into in vivo efficacy. A common approach to infer whether a model will respond in vivo is based on in vitro half‐maximal inhibitory concentration values (IC₅₀), but yields limited quantitative comparison between cell lines and drugs, potentially because cell division and death rates differ between cell lines and in vivo models. Other methods based either on mechanistic modeling or machine learning require molecular insights or extensive training data, limiting their use for early drug development. To address these challenges, we propose a mathematical model integrating in vitro growth rate inhibition values with pharmacokinetic parameters to estimate in vivo drug response. Upon calibration with a drug‐specific factor, our model yields precise estimates of tumor growth rate inhibition for in vivo studies based on in vitro data. We then demonstrate how our model can be used to study dosing schedules and perform sensitivity analyses. In addition, it provides meaningful metrics to assess association with genotypes and guide clinical trial design. By relying on commonly collected data, our approach shows great promise for optimizing drug development, better characterizing the efficacy of novel molecules targeting proliferation, and identifying more robust biomarkers of sensitivity while limiting the number of in vivo experiments.

Contribution of machine learning to tumor growth inhibition modeling for hepatocellular carcinoma patients under Roblitinib (FGF401) drug treatment

Machine learning (ML) opens new perspectives in identifying predictive factors of efficacy among a large number of patients’ characteristics in oncology studies. The objective of this work was to combine ML with population pharmacokinetic/pharmacodynamic (PK/PD) modeling of tumor growth inhibition to understand the sources of variability between patients and therefore improve model predictions to support drug development decisions. Data from 127 patients with hepatocellular carcinoma enrolled in a phase I/II study evaluating once‐daily oral doses of the fibroblast growth factor receptor FGFR4 kinase inhibitor, Roblitinib (FGF401), were used. Roblitinib  PKs was best described by a two‐compartment model with a delayed zero‐order absorption and linear elimination. Clinical efficacy using the longitudinal sum of the longest lesion diameter data was described with a population PK/PD model of tumor growth inhibition including resistance to treatment. ML, applying elastic net modeling of time to progression data, was associated with cross‐validation, and allowed to derive a composite predictive risk score from a set of 75 patients’ baseline characteristics. The two approaches were combined by testing the inclusion of the continuous risk score as a covariate on PD model parameters. The score was found as a significant covariate on the resistance parameter and resulted in 19% reduction of its variability, and 32% variability reduction on the average dose for stasis. The final PK/PD model was used to simulate effect of patients’ characteristics on tumor growth inhibition profiles. The proposed methodology can be used to support drug development decisions, especially when large interpatient variability is observed.

Hypothetical generalized framework for a new imaging endpoint of therapeutic activity in early phase clinical trials in brain tumors

Imaging response assessment is a cornerstone of patient care and drug development in oncology. Clinicians/clinical researchers rely on tumor imaging to estimate the impact of new treatments and guide decision making for patients and candidate therapies. This is important in brain cancer, where associations between tumor size/growth and emerging neurological deficits are strong. Accurately measuring the impact of a new therapy on tumor growth early in clinical development, where patient numbers are small, would be valuable for decision making regarding late-stage development activation. Current attempts to measure the impact of a new therapy have limited influence on clinical development, as determination of progression, stability or response does not currently account for individual tumor growth kinetics prior to the initiation of experimental therapies. Therefore, we posit that imaging-based response assessment, often used as a tool for estimating clinical effect, is incomplete as it does not adequately account for growth trajectories or biological characteristics of tumors prior to the introduction of an investigational agent. Here, we propose modifications to the existing framework for evaluating imaging assessment in primary brain tumors that will provide a more reliable understanding of treatment effects. Measuring tumor growth trajectories prior to a given intervention may allow us to more confidently conclude whether there is an anti-tumor effect. This updated approach to imaging-based tumor response assessment is intended to improve our ability to select candidate therapies for later-stage development, including those that may not meet currently sought thresholds for "response" and ultimately lead to identification of effective treatments.

Integrating a dynamic central metabolism model of cancer cells with a hybrid 3D multiscale model for vascular hepatocellular carcinoma growth

We develop here a novel modelling approach with the aim of closing the conceptual gap between tumour-level metabolic processes and the metabolic processes occurring in individual cancer cells. In particular, the metabolism in hepatocellular carcinoma derived cell lines (HEPG2 cells) has been well characterized but implementations of multiscale models integrating this known metabolism have not been previously reported. We therefore extend a previously published multiscale model of vascular tumour growth, and integrate it with an experimentally verified network of central metabolism in HEPG2 cells. This resultant combined model links spatially heterogeneous vascular tumour growth with known metabolic networks within tumour cells and accounts for blood flow, angiogenesis, vascular remodelling and nutrient/growth factor transport within a growing tumour, as well as the movement of, and interactions between normal and cancer cells. Model simulations report for the first time, predictions of spatially resolved time courses of core metabolites in HEPG2 cells. These simulations can be performed at a sufficient scale to incorporate clinically relevant features of different tumour systems using reasonable computational resources. Our results predict larger than expected temporal and spatial heterogeneity in the intracellular concentrations of glucose, oxygen, lactate pyruvate, f16bp and Acetyl-CoA. The integrated multiscale model developed here provides an ideal quantitative framework in which to study the relationship between dosage, timing, and scheduling of anti-neoplastic agents and the physiological effects of tumour metabolism at the cellular level. Such models, therefore, have the potential to inform treatment decisions when drug response is dependent on the metabolic state of individual cancer cells.

Analyzing the relationship between the vitamin D deficiency and COVID-19 mortality rate and modeling the time-delay interactions between body's immune healthy cells, infected cells, and virus particles with the effect of vitamin D levels

This paper presents some recent views on the aspects of vitamin D levels in relation to the COVID-19 infections and analyzes the relationship between the prevalence rates of vitamin D deficiency and COVID-19 death rates per million of various countries in Europe and Asia using the data from the PubMed database. The paper also discusses a new mathematical model of time-delay interactions between the body's immune healthy cells, infected cells, and virus particles with the effect of vitamin D levels. The model can be used to monitor the timely progression of healthy immune cells with the effects of the levels of vitamin D and probiotics supplement. It also can help to predict when the infected cells and virus particles free state can ever be reached as time progresses. The consideration of the time delay in the modeling due to effects of the infected cells or virus particles and the growth of healthy cells is also an important factor that can significantly change the outcomes of the body's immune cells as well as the infections.

Current State of Adjuvant Therapy for Melanoma: Less Is More, or More Is Better?

Advances in melanoma treatments over the past decade have changed the course of survival for patients. Several adjuvant therapies have been approved and are now considered standard of care for high-risk patients. These therapies have shown improvements for recurrence-free survival and distant metastases-free survival, but not overall survival, as the data are maturing. The 5-year recurrence-free survival in the COMBI-AD study, which compared dabrafenib and trametinib with placebo, was 65% and 58%, respectively. In the KEYNOTE-054 study, the recurrence-free survival at 3 years was 63.7% versus 41%. Despite these advances, approximately 50% of patients will succumb to their disease. Adjuvant therapy is considered potentially curative and avoids the morbidity of relapsed disease and the poor outcomes seen in metastatic disease. However, the lack of overall survival benefit in clinical trials of patients with high-risk stage II and stage III disease raises the question of whether it is more efficacious to treat when there is residual microscopic disease, or to wait until the disease recurs to avoid treating those who may have been cured by surgery alone. Immunotherapy also has the potential for substantial toxicity that may be lifelong; hence, discussion of risks and benefits of therapy is warranted because there should be less tolerance for substantial toxicity in the adjuvant setting. Adjuvant trials are needed that will integrate biomarkers to allow for better selection of patients who will truly benefit from adjuvant therapy.

Optimal Strategy and Benefit of Pulsed Therapy Depend On Tumor Heterogeneity and Aggressiveness at Time of Treatment Initiation

Therapeutic resistance is a fundamental obstacle in cancer treatment. Tumors that initially respond to treatment may have a preexisting resistant subclone or acquire resistance during treatment, making relapse theoretically inevitable. Here, we investigate treatment strategies that may delay relapse using mathematical modeling. We find that for a single-drug therapy, pulse treatment-short, elevated doses followed by a complete break from treatment-delays relapse compared with continuous treatment with the same total dose over a length of time. For tumors treated with more than one drug, continuous combination treatment is only sometimes better than sequential treatment, while pulsed combination treatment or simply alternating between the two therapies at defined intervals delays relapse the longest. These results are independent of the fitness cost or benefit of resistance, and are robust to noise. Machine-learning analysis of simulations shows that the initial tumor response and heterogeneity at the start of treatment suffice to determine the benefit of pulsed or alternating treatment strategies over continuous treatment. Analysis of eight tumor burden trajectories of breast cancer patients treated at Memorial Sloan Kettering Cancer Center shows the model can predict time to resistance using initial responses to treatment and estimated preexisting resistant populations. The model calculated that pulse treatment would delay relapse in all eight cases. Overall, our results support that pulsed treatments optimized by mathematical models could delay therapeutic resistance.

Tumor Growth Inhibition-Overall Survival (TGI-OS) Model for Subgroup Analysis Based on Post-Randomization Factors: Application for Anti-drug Antibody (ADA) Subgroup Analysis of Atezolizumab in the IMpower150 Study

Longitudinal changes of tumor size or tumor-associated biomarkers have been receiving growing attention as early markers of treatment benefits. Tumor growth inhibition-overall survival (TGI-OS) models represent mathematical frameworks used to establish a link from tumor size trajectory to survival outcome with the aim of predicting survival benefit with tumor data from a small number of subjects with a short follow-up time. In the present study, we applied the TGI-OS model to assess treatment benefit in the IMpower150 study for patients who exhibited development of anti-drug antibodies (ADA). Direct comparison between subgroups of the active arm [ADA positive (ADA +) and negative (ADA -) groups] to the entire control group is not appropriate, due to potential imbalances of baseline prognostic factors between ADA + and ADA - patients. Thus, the TGI-OS modeling framework was employed to adjust for differences in prognostic factors between the ADA subgroups to more accurately estimate the treatment benefits. After adjustment, the TGI-OS model predicted comparable hazard ratios (HRs) of OS between ADA + and ADA - subgroups, suggesting that the development of ADA does not have a clinically significant impact on the treatment benefit of atezolizumab.

A workflow for the joint modeling of longitudinal and event data in the development of therapeutics: Tools, statistical methods, and diagnostics

Clinical trials investigate treatment endpoints that usually include measurements of pharmacodynamic and efficacy biomarkers in early‐phase studies and patient‐reported outcomes as well as event risks or rates in late‐phase studies. In recent years, a systematic trend in clinical trial data analytics and modeling has been observed, where retrospective data are integrated into a quantitative framework to prospectively support analyses of interim data and design of ongoing and future studies of novel therapeutics. Joint modeling is an advanced statistical methodology that allows for the investigation of clinical trial outcomes by quantifying the association between baseline and/or longitudinal biomarkers and event risk. Using an exemplar data set from non‐small cell lung cancer studies, we propose and test a workflow for joint modeling. It allows a modeling scientist to comprehensively explore the data, build survival models, investigate goodness‐of‐fit, and subsequently perform outcome predictions using interim biomarker data from an ongoing study. The workflow illustrates a full process, from data exploration to predictive simulations, for selected multivariate linear and nonlinear mixed‐effects models and software tools in an integrative and exhaustive manner.

Anti-cancer treatment schedule optimization based on tumor dynamics modelling incorporating evolving resistance

Quantitative characterization of evolving tumor resistance under targeted treatment could help identify novel treatment schedules, which may improve the outcome of anti-cancer treatment. In this study, a mathematical model which considers various clonal populations and evolving treatment resistance was developed. With parameter values fitted to the data or informed by literature data, the model could capture previously reported tumor burden dynamics and mutant KRAS levels in circulating tumor DNA (ctDNA) of patients with metastatic colorectal cancer treated with panitumumab. Treatment schedules, including a continuous schedule, intermittent schedules incorporating treatment holidays, and adaptive schedules guided by ctDNA measurements were evaluated using simulations. Compared with the continuous regimen, the simulated intermittent regimen which consisted of 8-week treatment and 4-week suspension prolonged median progression-free survival (PFS) of the simulated population from 36 to 44 weeks. The median time period in which the tumor size stayed below the baseline level (T_TS<TS0) was prolonged from 52 to 60 weeks. Extending the treatment holiday resulted in inferior outcomes. The simulated adaptive regimens showed to further prolong median PFS to 56–64 weeks and T_TS<TS0 to 114–132 weeks under different treatment designs. A prospective clinical study is required to validate the results and to confirm the added value of the suggested schedules.

Mathematical Modeling the Time-Delay Interactions between Tumor Viruses and the Immune System with the Effects of Chemotherapy and Autoimmune Diseases

The immune system is the body’s defense against pathogens, which are complex living organisms found in many parts in the body including organs, tissues, cells, molecules, and proteins. When the immune system works properly, it can recognize and kill the abnormal cells and the infected cells. Otherwise, it can attack the body’s healthy cells even if there is no invader. Many researchers have developed immunotherapy (or cancer vaccines) and have used chemotherapy for cancer treatment that can kill fast-growing cancer cells or at least slow down tumor growth. However, chemotherapy drugs travel throughout the body and tend to kill both healthy cells and cancer cells. In this study, we consider the fact that chemotherapy can kill tumor cells and that the loss of the immune cells may at the same time stir up cancer growth. We present a dynamic time-delay tumor-immune model with the effects of chemotherapy drugs and autoimmune disease. The modeling results can be used to determine the progression of tumor cells in the human body with the effect of chemotherapy, autoimmune diseases, and time delays based on partial differential equations. It can also be used to predict when the tumor viruses’ free state can be reached as time progresses, as well as the state of the body’s healthy cells as time progresses. We also present a few numerical cases that illustrate that the model can be used to monitor the effects of chemotherapy drug treatment and the growth rate of tumor virus-infected cells and the autoimmune disease.

An overview of machine learning methods for monotherapy drug response prediction

For an increasing number of preclinical samples, both detailed molecular profiles and their responses to various drugs are becoming available. Efforts to understand, and predict, drug responses in a data-driven manner have led to a proliferation of machine learning (ML) methods, with the longer term ambition of predicting clinical drug responses. Here, we provide a uniquely wide and deep systematic review of the rapidly evolving literature on monotherapy drug response prediction, with a systematic characterization and classification that comprises more than 70 ML methods in 13 subclasses, their input and output data types, modes of evaluation, and code and software availability. ML experts are provided with a fundamental understanding of the biological problem, and how ML methods are configured for it. Biologists and biomedical researchers are introduced to the basic principles of applicable ML methods, and their application to the problem of drug response prediction. We also provide systematic overviews of commonly used data sources used for training and evaluation methods.

Bayesian inference of a non-local proliferation model

From a systems biology perspective, the majority of cancer models, although interesting and providing a qualitative explanation of some problems, have a major disadvantage in that they usually miss a genuine connection with experimental data. Having this in mind, in this paper, we aim at contributing to the improvement of many cancer models which contain a proliferation term. To this end, we propose a new non-local model of cell proliferation. We select data that are suitable to perform Bayesian inference for unknown parameters and we provide a discussion on the range of applicability of the model. Furthermore, we provide proof of the stability of posterior distributions in total variation norm which exploits the theory of spaces of measures equipped with the weighted flat norm. In a companion paper, we provide detailed proof of the well-posedness of the problem and we investigate the convergence of the escalator boxcar train (EBT) algorithm applied to solve the equation.

How translational modeling in oncology needs to get the mechanism just right

Translational model‐based approaches have played a role in increasing success in the development of novel anticancer treatments. However, despite this, significant translational uncertainty remains from animal models to patients. Optimization of dose and scheduling (regimen) of drugs to maximize the therapeutic utility (maximize efficacy while avoiding limiting toxicities) is still predominately driven by clinical investigations. Here, we argue that utilizing pragmatic mechanism‐based translational modeling of nonclinical data can further inform this optimization. Consequently, a prototype model is demonstrated that addresses the required fundamental mechanisms.

An integrative model of cancer cell differentiation with immunotherapy. Phys Biol 2021;18. [PMID: 34633296 DOI: 10.1088/1478-3975/ac2e72] [Citation(s) in RCA: 0] [Impact Index Per Article: 0]

In order to improve cancer treatments, cancer cell differentiation and immunotherapy are the subjects of several studies in different branches of interdisciplinary sciences. In this work, we develop a new population model that integrates other complementary ones, thus emphasizing the relationship between cancer cells at different differentiation stages and the main immune system cells. For this new system, specific ranges were found where transdifferentiation of differentiated cancer cells can occur. In addition, a specific therapy against cancer stem cells was analysed by simulating cytotoxic cell vaccines. In reference to the latter, the different combinations of parameters that optimize it were studied.

A Dynamic Model of Multiple Time-Delay Interactions between the Virus-Infected Cells and Body’s Immune System with Autoimmune Diseases

The immune system is a complex interconnected network consisting of many parts including organs, tissues, cells, molecules and proteins that work together to protect the body from illness when germs enter the body. An autoimmune disease is a disease in which the body’s immune system attacks healthy cells. It is known that when the immune system is working properly, it can clearly recognize and kill the abnormal cells and virus-infected cells. But when it doesn’t work properly, the human body will not be able to recognize the virus-infected cells and, therefore, it can attack the body’s healthy cells when there is no invader or does not stop an attack after the invader has been killed, resulting in autoimmune disease.; This paper presents a mathematical modeling of the virus-infected development in the body’s immune system considering the multiple time-delay interactions between the immune cells and virus-infected cells with autoimmune disease. The proposed model aims to determine the dynamic progression of virus-infected cell growth in the immune system. The patterns of how the virus-infected cells spread and the development of the body’s immune cells with respect to time delays will be derived in the form of a system of delay partial differential equations. The model can be used to determine whether the virus-infected free state can be reached or not as time progresses. It also can be used to predict the number of the body’s immune cells at any given time. Several numerical examples are discussed to illustrate the proposed model. The model can provide a real understanding of the transmission dynamics and other significant factors of the virus-infected disease and the body’s immune system subject to the time delay, including approaches to reduce the growth rate of virus-infected cell and the autoimmune disease as well as to enhance the immune effector cells.

Supermodeling in predictive diagnostics of cancer under treatment

Classical data assimilation (DA) techniques, synchronizing a computer model with observations, are highly demanding computationally, particularly, for complex over-parametrized cancer models. Consequently, current models are not sufficiently flexible to interactively explore various therapy strategies, and to become a key tool of predictive oncology. We show that, by using supermodeling, it is possible to develop a prediction/correction scheme that could attain the required time regimes and be directly used to support decision-making in anticancer therapies. A supermodel is an interconnected ensemble of individual models (sub-models); in this case, the variously parametrized baseline tumor models. The sub-model connection weights are trained from data, thereby incorporating the advantages of the individual models. Simultaneously, by optimizing the strengths of the connections, the sub-models tend to partially synchronize with one another. As a result, during the evolution of the supermodel, the systematic errors of the individual models partially cancel each other. We find that supermodeling allows for a radical increase in the accuracy and efficiency of data assimilation. We demonstrate that it can be considered as a meta-procedure for any classical parameter fitting algorithm, thus it represents the next - latent - level of abstraction of data assimilation. We conclude that supermodeling is a very promising paradigm that can considerably increase the quality of prognosis in predictive oncology.

Epigenetic instability may alter cell state transitions and anticancer drug resistance

Drug resistance is a significant obstacle to successful and durable anti-cancer therapy. Targeted therapy is often effective during early phases of treatment; however, eventually cancer cells adapt and transition to drug-resistant cells states rendering the treatment ineffective. It is proposed that cell state can be a determinant of drug efficacy and manipulated to affect the development of anticancer drug resistance. In this work, we developed two stochastic cell state models and an integrated stochastic-deterministic model referenced to brain tumors. The stochastic cell state models included transcriptionally-permissive and -restrictive states based on the underlying hypothesis that epigenetic instability mitigates lock-in of drug-resistant states. When moderate epigenetic instability was implemented the drug-resistant cell populations were reduced, on average, by 60%, whereas a high level of epigenetic disruption reduced them by about 90%. The stochastic-deterministic model utilized the stochastic cell state model to drive the dynamics of the DNA repair enzyme, methylguanine-methyltransferase (MGMT), that repairs temozolomide (TMZ)-induced O6-methylguanine (O6mG) adducts. In the presence of epigenetic instability, the production of MGMT decreased that coincided with an increase of O6mG adducts following a multiple-dose regimen of TMZ. Generation of epigenetic instability via epigenetic modifier therapy could be a viable strategy to mitigate anticancer drug resistance.

Musiré: multimodal simulation and reconstruction framework for the radiological imaging sciences

A software-based workflow is proposed for managing the execution of simulation and image reconstruction for SPECT, PET, CBCT, MRI, BLI and FMI packages in single and multimodal biomedical imaging applications. The workflow is composed of a Bash script, the purpose of which is to provide an interface to the user, and to organize data flow between dedicated programs for simulation and reconstruction. The currently incorporated simulation programs comprise GATE for Monte Carlo simulation of SPECT, PET and CBCT, SpinScenario for simulating MRI, and Lipros for Monte Carlo simulation of BLI and FMI. Currently incorporated image reconstruction programs include CASToR for SPECT and PET as well as RTK for CBCT. MetaImage (mhd) standard is used for voxelized phantom and image data format. Meshlab project (mlp) containers incorporating polygon meshes and point clouds defined by the Stanford triangle format (ply) are employed to represent anatomical structures for optical simulation, and to represent tumour cell inserts. A number of auxiliary programs have been developed for data transformation and adaptive parameter assignment. The software workflow uses fully automatic distribution to, and consolidation from, any number of Linux workstations and CPU cores. Example data are presented for clinical SPECT, PET and MRI systems using the Mida head phantom and for preclinical X-ray, PET and BLI systems employing the Digimouse phantom. The presented method unifies and simplifies multimodal simulation setup and image reconstruction management and might be of value for synergistic image research. This article is part of the theme issue 'Synergistic tomographic image reconstruction: part 2'.

Study of Combinatorial Drug Synergy of Novel Acridone Derivatives With Temozolomide Using in-silico and in-vitro Methods in the Treatment of Drug-Resistant Glioma

Drug resistance is one of the critical challenges faced in the treatment of Glioma. There are only limited drugs available in the treatment of Glioma and among them Temozolomide (TMZ) has shown some effectiveness in treating Glioma patients, however, the rate of recovery remains poor due to the inability of this drug to act on the drug resistant tumor sub-populations. Hence, in this study three novel Acridone derivative drugs AC2, AC7, and AC26 have been proposed. These molecules when combined with TMZ show major tumor cytotoxicity that is effective in suppressing growth of cancer cells in both drug sensitive and resistant sub-populations of a tumor. In this study a novel mathematical model has been developed to explore the various drug combinations that may be useful for the treatment of resistant Glioma and show that the combinations of TMZ and Acridone derivatives have a synergistic effect. Also, acute toxicity studies of all three acridone derivatives were carried out for 14 days and were found safe for oral administration of 400 mg/kg body weight on albino Wistar rats. Molecular Docking studies of acridone derivatives with P-glycoprotein (P-gp), multiple resistant protein (MRP), and O6-methylguanine-DNA methyltransferase (MGMT) revealed different binding affinities to the transporters contributing to drug resistance. It is observed that while the Acridone derivatives bind with these drug resistance causing proteins, the TMZ can produce its cytotoxicity at a much lower concentration leading to the synergistic effect. The in silico analysis corroborate well with our experimental findings using TMZ resistant (T-98) and drug sensitive (U-87) Glioma cell lines and we propose three novel drug combinations (TMZ with AC2, AC7, and AC26) and dosages that show high synergy, high selectivity and low collateral toxicity for the use in the treatment of drug resistant Glioma, which could be future drugs in the treatment of Glioblastoma.

Analysis of the effectiveness of the treatment of solid tumors in two cases of drug administration

A complete stability analysis of the equilibrium solutions of a system modeling tumor chemotherapy is performed in two cases of administration of the treatment, by continuous infusion and by periodic infusion. Several numerical simulations illustrate and complement the theory.